Comptes Rendus
Géométrie birationnelle
A remark on the rank of finite p-groups of birational automorphisms
Comptes Rendus. Mathématique, Volume 358 (2020) no. 7, pp. 827-829.

Dans cette note, nous améliorons un résultat de Prokhorov et Shramov sur le rang des p-sous-groupes finis du groupe des transformations birationnelles d’une variété rationnellement connexe. Des exemples connus montrent que les bornes obtenues sont optimales dans de nombreux cas.

In this note, we improve a result of Prokhorov and Shramov on the rank of finite p-subgroups of the group of birational transformations of a rationally connected variety. Known examples show that the bounds obtained are optimal in many cases.

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DOI : 10.5802/crmath.93

Jinsong Xu 1

1 Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, No.111, Ren’ai Road, SIP, Suzhou, Jiangsu Province, China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Jinsong Xu. A remark on the rank of finite $p$-groups of birational automorphisms. Comptes Rendus. Mathématique, Volume 358 (2020) no. 7, pp. 827-829. doi : 10.5802/crmath.93. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.93/

[1] Arnaud Beauville p-Elementary subgroups of the Cremona group, J. Algebra, Volume 314 (2007) no. 2, pp. 553-564 | DOI | MR | Zbl

[2] Caucher Birkar Singularities of linear systems and boundedness of Fano varieties (2016) (https://arxiv.org/abs/1609.05543)

[3] Olivier Haution Fixed point theorems involving numerical invariants, Compos. Math., Volume 155 (2019) no. 2, pp. 260-288 | DOI | MR | Zbl

[4] János Kollár Rational Curves on Algebraic Varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., 32, Springer, 1995 | Zbl

[5] Alexandra Kuznetsova Finite 3-subgroups in Cremona group of rank 3 (2020) (https://arxiv.org/abs/2001.01308)

[6] Vladimir L. Popov Jordan Groups and Automorphism Groups of Algebraic Varieties, Automorphisms in Birational and Affine Geometry. Papers based on the presentations at the conference, Levico Terme, Italy, October 29 – November 3, 2012 (Springer Proceedings in Mathematics & Statistics), Volume 79 (2014), pp. 185-213 | MR | Zbl

[7] Yuri G. Prokhorov p-elementary subgroups of the Cremona group of rank 3, Classification of algebraic varieties. Based on the conference on classification of varieties, Schiermonnikoog, Netherlands, May 2009 (EMS Series of Congress Reports), European Mathematical Society, 2011, pp. 327-338 | MR | Zbl

[8] Yuri G. Prokhorov 2-Elementary Subgroups of the Space Cremona Group, Automorphisms in Birational and Affine Geometry. Papers based on the presentations at the conference, Levico Terme, Italy, October 29 – November 3, 2012 (Springer Proceedings in Mathematics & Statistics), Volume 79 (2014), pp. 215-229 | MR | Zbl

[9] Yuri G. Prokhorov; Constantin Shramov Jordan property for groups of birational selfmaps, Compos. Math., Volume 150 (2014) no. 12, pp. 2054-2072 | DOI | MR | Zbl

[10] Yuri G. Prokhorov; Constantin Shramov Jordan property for Cremona groups, Am. J. Math., Volume 138 (2016) no. 2, pp. 403-418 | DOI | MR | Zbl

[11] Yuri. G. Prokhorov; Constantin Shramov Jordan constant for Cremona group of rank 3, Mosc. Math. J., Volume 17 (2017) no. 3, pp. 457-509 | DOI | MR | Zbl

[12] Yuri. G. Prokhorov; Constantin Shramov p-subgroups in the space Cremona group, Math. Nachr., Volume 291 (2017) no. 8-9, pp. 1374-1389 | DOI | MR | Zbl

[13] Jean-Pierre Serre A Minkowski-style bound for the orders of the finite subgroups of the Cremona group of rank 2 over an arbitrary field, Mosc. Math. J., Volume 9 (2009) no. 1, pp. 193-208 | MR | Zbl

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